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Moon Search Algorithms for NASA's Dawn Mission to Asteroid Vesta

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Moon Search Algorithms for NASA's Dawn Mission to Asteroid Vesta Moon Search Algorithms for NASA’s Dawn Mission to Asteroid Vesta Nargess Memarsadeghi*a, Lucy A. McFaddena, David R. Skillmana, Brian McLeanb, Max Mutchlerb, Uri Carsenty c, Eric E. Palmer d, and the Dawn Mission’s Satellite Working Group aNASA Goddard Space Flight Center, Greenbelt, Maryland, USA bSpace Telescope Science Institute, Baltimore, Maryland, USA cDLR, Institute of the Planetary Research, Berlin, Germany dPlanetary Science Institute, Tucson, Arizona, USA ABSTRACT A moon or natural satellite is a celestial body that orbits a planetary body such as a planet, dwarf planet, or an asteroid. Scientists seek understanding the origin and evolution of our solar system by studying moons of these bodies. Additionally, searches for satellites of planetary bodies can be important to protect the safety of a spacecraft as it approaches or orbits a planetary body. If a satellite of a celestial body is found, the mass of that body can also be calculated once its orbit is determined. Ensuring the Dawn spacecraft’s safety on its mission to the asteroid (4) Vesta primarily motivated the work of Dawn’s Satellite Working Group (SWG) in summer of 2011. Dawn mission scientists and engineers utilized various computational tools and techniques for Vesta’s satellite search. The objectives of this paper are to 1) introduce the natural satellite search problem, 2) present the computational challenges, approaches, and tools used when addressing this problem, and 3) describe applications of various image processing and computational algorithms for performing satellite searches to the electronic imaging and computer science community. Furthermore, we hope that this communication would enable Dawn mission scientists to improve their satellite search algorithms and tools and be better prepared for performing the same investigation in 2015, when the spacecraft is scheduled to approach and orbit the dwarf planet (1) Ceres. Keywords: Planetary sciences, astronomy, natural satellite search, Pluto, Dawn mission, asteroid (4) Vesta, image registration, filtering. 1. INTRODUCTION Planets and dwarf planets follow elliptical paths with the Sun at one of its two foci. Asteroids, small bodies in the Solar System primarily located between Mars and Jupiter also orbit the Sun [1]. A moon or natural satellite orbits a planet, dwarf planet, or asteroid, called its primary [2]. Scientists can learn about the origin, early history, and evolution of our solar system by searching for and studying moons of planetary bodies [1-6]. From the orbital characteristics of natural satellites and combining Newton’s and Kepler’s laws the mass of the primary asteroid can be calculated [7]. This can be done from the Earth based telescopes without the need for in situ spacecraft measurements [4-6]. Scientists also study planetary bodies using robotic spacecraft [7-8]. Protecting the spacecraft from collision with a natural satellite was the primary motivation for the satellite search conducted as the Dawn spacecraft went into orbit around the main belt asteroid (4) Vesta. Secondary motivation was scientific investigation of the asteroid, which we will refer to as Vesta for the remainder of this paper. The Dawn mission, part of NASA’s Discovery program, was launched on September 27, 2007. The mission’s primary goals are to study Vesta and dwarf planet (1) Ceres as precursors to planetary bodies. After a four-year, slow and steady approach, the spacecraft finally entered an orbit around Vesta in July 2011, making Dawn the first probe to orbit an object in the Main Asteroid Belt between Mars and Jupiter. Figure 1(a) represents the locations of Vesta and Ceres schematically with the Sun at a focus, the paths of the planets drawn as ellipses and the position of the main belt asteroids at a moment in time between Mars and Jupiter [1]. Figure 1(b) displays the Dawn mission’s timeline with * Corresponding author: Nargess Memarsadeghi, NASA GSFC, Mail Stop 587, Greenbelt, MD, 20771. Email: [email protected]. Tel: 301-286-2938. respect to the positions of the planets, depicting the path of the spacecraft from its launch in 2007 to entering and exiting Vesta’s and Ceres’s orbits, and finally the end of the mission in 2015 [8]. Dawn mission’s Satellite Working Group utilized various computational tools and techniques for Vesta’s satellite search in 2011. The objectives of this paper are to 1) introduce the natural satellite search problem, 2) its computational challenges, and 3) applications of various image processing and computational algorithms for performing satellite search to the electronic imaging and computer science community. We achieve these goals by presenting two case studies, one duplicating a past satellite search performed on Pluto and another on our recent work on Vesta. Furthermore, we hope that this communication would enable Dawn mission scientists to improve their satellite search algorithms and tools to better prepare them for performing the same investigation in 2015, when the spacecraft is scheduled to approach and enter an orbit around the dwarf planet (1) Ceres. (a) (b) Figure 1- (a) Plane view of the position of Vesta and Ceres with respect to our solar system and the Main Asteroid Belt between Mars and Jupiter [1]. (b) Dawn mission’s timeline from its launch in 2007 to the end of mission in 2015 [8]. The remainder of this paper is organized as follows. First, we introduce the natural satellite search problem in Section 2. Then, in Section 3, we present a brief survey of the past work done for discovery of natural satellites via electronic imaging. We review computational methods, tools, and issues for moon search approaches in Section 4. In particular, we present a case study on verification of the discovery of two of Pluto’s moons, Nix and Hydra. Finally, in Section 5 we report on various tools and algorithms that were utilized by Dawn mission’s SWG for Vesta’s satellite search in 2011. These algorithms include image registration, filtering, and capabilities provided by software packages called astrometry.net [9] and Astrometrica [10]. We will also mention shortcomings of satellite search approaches due to limitations imposed by specific mission designs and science objectives as well as related computational challenges , which could potentially be addressed by the electronic imaging community. Section 6 concludes the paper. 2. SATELLITE SEARCH PROBLEM In this section we describe how astronomers search for moons of planetary bodies or perform a satellite search. Moons or satellites of a celestial body are confined to a region of that body’s gravitational influence. Scientists approximate the region where the gravitational force of the primary body (e.g. Earth, Mars) dominates that of the more massive yet more distant body, the Sun, as a spherical region called the Hill sphere [2–6]. When the primary body, with mass mp rotates around the Sun with mass M, the radius of the Hill sphere for the primary body is calculated as 1 ⎛ m ⎞3 p (1) rH = ap ⎜ ⎟ ⎝ 3M ⎠ where a p is the semi-major axis of the primary’s orbit around the Sun (e.g. Earth-Sun, Mars-Sun, distance). Considering a mass for Pluto of 1.25×1022 kilograms and a semi-major axis for its orbit around the Sun and a solar mass 1 ⎛ 1.25 ×1022 ⎞3 of 1.99×1030 kg, Pluto’s Hill sphere is R = 5906.38 ×106 ⎜ ⎟ = 7.5561×106 H ⎜ 30 ⎟ ⎝ 3×1.99 ×10 ⎠ kilometers. Vesta’s Hill sphere in May 2007 was measured to be 488 Vesta radii (with Vesta radius being 265 kilometers) or 129,320 kilometers in radius [11], less than two percent of that of Pluto! Astronomers consider several criteria for validating a potential moon detection as a natural satellite of its primary: 1. It is expected to reside within the primary’s Hill sphere. 2. It should be an unknown object and not be listed in any star catalogue. 3. For high resolution data, it should have a point spread function. That is, it should not appear as a spike in only one pixel. Furthermore, it should have the correct point spread function (PSF), one matching that of the observing camera. 4. It should be observed more than once and in consecutive frames. 5. It should obey Newton’s and Kepler’s laws of motion. Usually the first three criteria can be verified with a single data set. The fourth criterion requires consecutive observations of the same area. Potential moons that meet the first four criteria are identified. Then, follow-up observations are made at a later time to verify the discovery. That was the case for 2006 Hubble Space Telescope data where follow-up observations of Pluto were made to verify the discovery of two of its moons, Nix and Hydra, that were first observed in 2005. 3. LITERATURE SURVEY Searching for moons around planets has a long history. For example, it was in 1878 when Asaph Hall discovered two moons of Mars which were later named Phobos and Deimos, with the 26-inch Refractor Telescope at the Naval Observatory in Washington D.C. [12-13]. With advances in imaging instruments and technologies as well as robotic exploration of the outer solar system, there has been an increase in satellite search and discoveries around many planets including Jupiter, Saturn, Uranus, Neptune, and Pluto [2-6] with some of the outer planets having more than 50 natural satellites. No additional satellites of Mars have been found. Pluto and its moons have a fascinating story. It was in 1930 that Clyde Tombaugh discovered Pluto, and then Pluto’s largest moon, Charon, was discovered in 1978 [14]. It was much later in 2005 that two smaller moons, Nix and Hydra, were discovered and later verified in 2006 using observations of the Hubble Space Telescope [15-16].
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